Abstract
We prove that every place P of an algebraic function field F | K of arbitrary characteristic admits local uniformization, provided that the sum of the rational rank of its value group and the transcendence degree of its residue field FP over K is equal to the transcendence degree of F | K , and the extension F P | K is separable. We generalize this result to the case where P dominates a regular local Nagata ring R ⊆ K of Krull dimension dim R ⩽ 2 , assuming that the valued field ( K , v P ) is defectless, the factor group v P F / v P K is torsion-free and the extension of residue fields F P | K P is separable. The results also include a form of monomialization.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Annales Scientifiques de l’École Normale Supérieure
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.